Question

I'm currently researching the intermodal distance of transverse and axial modes in optical cavities. But the equation defining the longitudinal separation contains the +- sign, does this imply that both those positions there are longitudinal modes?

Δν_transverse=c/(2L)[cos−1(±√(g_1g_2))/π]

Furthermore, do the higher-order transverse modes of say; axial mode 1, overlap with the positions of higher order axial modes?

Answer 1

The ± sign in the equation indicates two possible positions for longitudinal modes in optical cavities. Higher-order transverse modes can overlap with the positions of higher-order axial modes when the conditions for constructive interference are satisfied.

Step-by-step explanation:

The equation Δν_transverse=c/(2L)[cos−1(±√(g_1g_2))/π] represents the longitudinal separation in optical cavities. The ± sign in the equation indicates that there are two possible positions for longitudinal modes. It implies that there are both positive and negative longitudinal modes.

Higher-order transverse modes, such as axial mode 1, can overlap with the positions of higher-order axial modes. This occurs when the conditions for constructive interference, as given by the Bragg equation, are satisfied, where d is the distance between slits in the grating, λ is the wavelength of light, and m is the order of the maximum.